The Wave Model. RCPWAVE 



24. The RCPWAVE model is a linear short-wave model which considers 

 transformation of surface gravity waves in shallow water including the pro- 

 cesses of shoaling, refraction, and diffraction due to bathymetry and allows 

 for wave breaking and decay within the surf zone (the region shoreward of the 

 breaker line). Unlike traditional wave-ray tracing methods, the model uses a 

 rectilinear grid so that model output in the form of wave height, direction, 

 and wave number is available at the centers of the grid cells. This avail- 

 ability is highly advantageous since the information can be used directly as 

 input to the wave-induced current and sediment transport models, and the prob- 

 lem of caustics due to crossing of wave rays is avoided. The description of 

 RCPWAVE that follows is extracted from a report by Ebersole, Cialone, and 

 Prater (1986). 



25. Berkhoff (1972 and 1976) derived an elliptic equation approximating 

 the complete wave transformation process for linear waves over an arbitrary 

 bathymetry constrained only to have mild bottom slopes (thus the designation 

 mild slope equation (Smith and Sprinks 1975)). The mild slope equation can be 

 expressed in the following form: 



|_(ec |^)-^^(cc M)+a2!s* = (24) 



8x y g 8x/ 9y \ g 8y/ c ^ 



where 



(t)(x,y) = complex velocity potential 



2 

 T 



a = wave angular frequency = ;p— 



T = wave period 

 c(x,y) = wave celerity = -r 



c (x,y) = group velocity = -rr 

 k(x,y) = wave number given by the dispersion relation 



a = gk tanh(kh) (25) 



26. Numerical solution of this equation for the velocity potential 

 field is an effective means for solving the complete wave propagation problem. 



21 



